We present the &mu; -calculus, a syntax for &lambda;-calculus + control operators exhibiting symmetries such as program/context and call-by-name/call-by-value. This calculus is derived from implicational Gentzen's sequent calculus <i>LK</i>, a key classical logical system in proof theory. Under the Curry-Howard correspondence between proofs and… (More)
The λ&sgr;-calculus is a refinement of the λ-calculus where substitutions are manipulated explicitly. The λ&sgr;-calculus provides a setting for studying the theory of substitutions, with pleasant mathematical properties. It is also a useful bridge between the classical λ-calculus and concrete implementations.
We consider the Curry-Howard-Lambek correspondence for effectful computation and resource management, specifically proposing polarised calculi together with presheaf-enriched adjunction models as the starting point for a comprehensive semantic theory relating logical systems, typed calculi, and categorical models in this context. Our thesis is that the… (More)